Oppenheimer-Snyder Model Research Articles

Astrophysical shock-wave solutions of the Einstein equations.

We construct exact, spherically symmetric, shock-wave solutions of the Einstein equations for a perfect fluid. The solutions are obtained by matching a Friedmann-Roberson-Walker metric (a cosmological model for the Universe) to a static Oppenheimer-Tolman metric (a model for the interior of a star) across a shock-wave interface. This is in the spirit of Oppenheimer and Snyder, except, in contrast with the Oppenheimer-Snyder model, the pressure p is nonzero. Our shock-wave solutions model the general relativistic version of an explosion into a static, singular, isothermal sphere. Shock waves introduce time irreversibility, loss of information, decay, dissipation, and increase of entropy into the dynamics of a perfect fluid in general relativity. As a corollary, we also obtain a different Oppenheimer-Snyder model for the case p==0.

Shock-wave solutions of the einstein equations: The Oppenheimer-Snyder model of gravitational collapse extended to the case of non-zero pressure

Shock-wave solutions of the einstein equations: The Oppenheimer-Snyder model of gravitational collapse extended to the case of non-zero pressure

Hawking Radiation Due to a Collapsing Star. II: Collapsing Shells in Two-Dimensional Space-Times

We ·investigate the energy flux of the Hawking radiation due to collapsing shells in two· dimensional space· times seen by a distant observer during the entire stage from its onset to the final steady state. The space·times considered are those obtained from four-dimensional ones containing a collapsing shell to form a black hole. In the first model the trajectory of the shell is taken to be the radial geodesic with respect to the exterior Schwarzschild geometry, while the second model treats a freely collapsing shell of dust. It is shown that the behavior of the flux in both models is quite similar to that of the Oppenheimer-Snyder model in the entire stage of evolution. The third model considers a shell of dust falling into an eternal black hole to form a new black hole. As the shell starts to fall the flux suddenly rises and then monotonically decreases to the thermal value corresponding to the new black hole. We also show that the energy flux radiated to the inside of the shell is negative in each of the three models. § 1. . Introduction In the previous paper!) (hereafter referred to as I) we calculated the stress energy: tensor T plI of the Hawking radiation in the case of a two-dimensional version of the Oppenheimer-Snyder (O-S) model which is the basic standard model of the gravita­ tional collapse, and investigated especially the energy flux seen by a distant observer in the entire stage of evolution. There we found that its behavior is insensitive to changes in the initial radius Ri of the star. It is interesting to investigate other basic models and compare the results to clarify how the differences between the models are reflected in the behavior of the energy flux. In this paper, we consider the models of collapsing shell which are frequently employed in dealing with the Hawking radia­ tion. 2 )-4) The quantum field is taken to be the massless real scalar field as in I. The models of collapsing shell make a contrast to O-S model because the mass of the collapsing is concentrated in the shell, while the mass distribution in the star of the O-S model is homogeneous. We will begin, in § 2, with an application of a simple method of calculating T plI due to moving shells 5 ) to a case in which a shell

Gravitational collapse in free fall of a slowly rotating star

The Oppenheimer-Snyder model of a spherically symmetric collapse in free fall is generalized to the case in which the star possesses a small rotation. The exterior geometry is chosen to be the Kerr metric in synchronous coordinates, discarding terms of the order (a/r)2. The interior geometry is constructed by adding to the exact metric of the nonrotating case an off-diagonal first-order term in the parametera. This term is determined in part by requiring the validity of the junction conditions at the star's surface and, also, by demanding the conserved angular momentum of the source be equal toMa, in agreement with the value measured by a distant observer. The resulting stress-energy tensor describes a homogeneous, pressureless, ideal fluid (dust) nonuniformly rotating relative to the synchronous frame, which is no longer comoving with the stellar matter. The dynamics of collapse is qualitatively the same as in the spherically symmetric case. Again the star's surface crosses the event horizon when the mass density is finite everywhere, and space-time has not developed any singularity as viewed by freely falling observers at rest in the synchronous frame.

Some exact models of inhomogeneous dust collapse

Three classes of irrotational-dust-collapse models with high symmetries are studied. The interior collapsing solution is joined smoothly onto an exterior static vacuum. The spherical model is just a generalization of the Oppenheimer-Snyder model. A black hole is formed in this case. The plane-symmetric model turns out to either have negative gravitating mass and bounce, never reaching the singularity, or have no static exterior. In the latter case all we get for the exterior is a Kasner universe. In the cylindrical case, however, we succeed in constructing a model that, starting with initially regular conditions, collapses into the naked singularity of an external static field.